Women aren't funny. Christopher Hitchens made the claim last year, but fortunately Tina Fey didn't get the fax. Fey is the producer and star of America's latest hit movie comedy Baby Mama, which has gone straight to the top of the American box office.

The success establishes her as the most powerful woman in American comedy and may finally convince Hollywood executives that women really can be brainy, hilarious, and commercially popular. The film, a female buddy comedy in which Fey's character finds a hilariously inappropriate surrogate mother for her baby, took

$18.3 million in its first weekend. (Baby Mama is Fey's second number-one hit. The first was the deliciously bitchy 2004 high-school comedy Mean Girls, starring Lindsay Lohan, which Fey wrote, produced and also starred in.) What's even more significant is that Baby Mama easily beat comedies aimed at Hollywood's preferred and pampered audience - horny teenage boys. Women made up 68 per cent of the audience, and 55 per cent of them were older than 25.

Baby Mama features Fey as Kate Holbrook, a 37-year-old, unmarried, politically correct, over-achieving executive for an organic-foods company. She hires Angie, played by her Saturday Night Live co-star Amy Poehler, to have her baby. Much of the comedy comes when Kate and Angie, a gum-chewing, working-class party girl, become 'womb mates', moving in together. Imagine a 21st-century version of The Odd Couple. Their dysfunctional but often very funny relationship makes Baby Mama 'such a welcome alternative to the desperation and self-loathing of the Judd Apatow canon, or the compulsive verbosity of Juno', says Ann Hornaday, film critic of the Washington Post

Fey, who came to prominence on Saturday Night Live, the long-running TV sketch show, is already one of the most important figures in US television. She's the producer and star of the sitcom 30 Rock, which won an Emmy last year, beating The Office and Ugly Betty. Set behind the scenes of a Saturday Night Live-like TV show on which she plays the unattached head writer Liz Lemon, it's been hailed as the 'best sitcom since Seinfeld'. The combination of genius casting, including Alec Baldwin as a controlling TV executive, with dense scripts which combine high and lowbrow humour means it has the kind of devoted following long overdue for an American network comedy series (critics rave about it, saying they watch it twice in order to catch all the jokes). Although Fey is thrilled at the success of Baby Mama, what really makes her happy is that Lemon has been called 'the most realistic single woman on television'.

'We strive to make her realistic to the point of embarrassment,' says Fey, who acknowledges that Lemon is an unmarried version of herself. (Fey, 38, has been married for seven years to Jeff Richmond, a music supervisor who works with her. They have a two-year-old daughter.) 'We're just trying to show the underbelly of being a real woman. But it's TV, so I'm sure there are things that are heightened. I mean, she did steal a baby once.'

Robert Thompson, professor of popular culture at Syracuse University, believes that what's most remarkable about Tina Fey's success is that she 'has carved out a really new female comedy character, this pretty yet insecure intellectual. Fey is short, she's got glasses and she's insecure. It is really refreshing and not at all typical.'

Donna Langley, president of production at Universal Studios, which produced Baby Mama, believes that Fey has a unique generational appeal. 'Tina is so connected to the zeitgeist,' says Langley, referring not just to the success of Baby Mama and 30 Rock, but to a Fey sketch on Saturday Night Live in March which had a remarkable and pivotal impact on the Democratic presidential campaign. (Fey left Saturday Night Live in 2006, but returns to the show occasionally.) The sketch she wrote and delivered has been credited for single-handedly reviving the fortunes of Hillary Clinton, then all but counted out after a series of devastating primary defeats. It showed the press being ridiculously deferential to Barack Obama.

'If anybody saw Saturday Night Live,' Hillary said in a debate soon after, 'maybe we should ask Barack if he's comfortable and needs another pillow.' It was the last line of the sketch, which the New York Times described as 'a brilliant girl-power endorsement from Tina Fey', which gave Hillary and her floundering campaign heart, by making a political virtue out of what has been seen as her greatest failing. 'Bitches get stuff done,' snapped Fey. 'Bitch is the new black.'

Shortly after that, Fey's status as the most important woman in comedy was confirmed by her appearance on the front cover of American Marie Claire magazine which normally features young Hollywood starlets, not 38-year-old spectacle-wearing, self-confessed geeks.

Fey seems to have fashioned her comic persona around her glasses. She first started using them when she joined Saturday Night Live in 1995, discovering before her first show that she needed them to read cue cards. She quickly realised that they give her the apparent moral authority to smile sweetly as she sticks a knife into the backs of the mighty, the pompous and the idiotic.

Recently, for instance, she called Paris Hilton 'a piece of shit' who has 'hands like a tranny', and is 'a terrible role model and a terrible young woman. You can buy videotapes in which you can see her bejanis.' (As a comedy sideline, Fey has devised many TV-acceptable euphemisms for female genitalia, her favourite, and ours', being 'cooter'. One of her sketches for Saturday Night Live was called 'Talkin 'Bout 'Ginas', a parody of The Vagina Monologues

But as the most famous - and most fetishised - spectacle-wearer in America, Fey plays down her status as the thinking man's sex symbol. 'Glasses make anyone look smarter,' says Fey, who can seem reserved in person. 'You put glasses on Woody Harrelson in Indecent Proposal and he's an architect. You put a pair of glasses on Denise Richards and she's a palaeontologist.'

The day Baby Mama opens, I ask Lorne Michaels, creator and producer of Saturday Night Live and co-producer of Baby Mama, what he feels is most distinctive about Fey and her humour. 'She has a very clear take on things,' he says. 'It always comes from a place of intelligence and there is just an edge to it. It's not fearful. It's strong and confident and you recognise the voice and most of the time you agree with it.'

That's interesting, I say, because people who know her well say she's quite shy. 'As a person, yes, I think that is so,' he says, 'but she projects a confidence. I have never seen her face a challenge that she didn't pull off. She won't give up until it's good. She has impossibly high standards.'

If Tina Fey's self-effacing appearance is unusual for a female comedian, her background and temperament seem particularly ill-suited to her chosen profession. Coming from a solidly upper-middle-class, stable Greek-American family in Pennsylvania, Fey was an unapologetic geek and straight-A student, editor of the school newspaper, in the drama club and member of the choir. She had trouble fitting in.

'I had a pretty rough puberty,' she says. 'Growing up as a girl is always traumatising, especially when you have the deadly combination of greasy skin and getting your boobs at 10. But somewhere around the fifth or seventh grade I figured out that I could ingratiate myself to people by making them laugh. I was trying to make them like me. But after a while it became part of my identity.'

She now acknowledges that much of the fabulous bitchiness of Mean Girls, which she wrote, came from her own high-school experience. Lindsay Lohan plays a naive teenager who has been home-schooled and is then plunged into the cliquey gender rituals of American high school.

'I ate weaker girls for breakfast,' Fey admits. 'I really was a snarky girl. My whole thing was, if I really liked a guy and he had the audacity to like someone else instead of me, I would hate that girl and devote hours and hours of time to picking her apart and talking about her behind her back and canvassing my friends to dislike her.'

At the University of Virginia, where she studied drama, Fey was again not part of the cool crowd. She disapproved of the heavy drinking, drug-taking and sexual promiscuity in which many of her fellow students indulged. Today she's proud that she's never taken drugs, except in childbirth.

'I want to be on record saying this, so my daughter can see it one day in the future. I have never done any drugs! I am extremely square and obedient in nature!'

After university, Fey went to Chicago, joining the Second City troupe, renowned for improvisational comedy. She went because she knew a number of alumni had graduated to Saturday Night Live, including John Belushi and Bill Murray. Fey honed her particular brand of humour there, specialising in especially lewd and caustic routines. In one sketch, she imagined Catherine the Great complaining about the unfairness of life: 'You can be a murderous tyrant and the world will remember you fondly. But fuck one horse and you're a horse-fucker for all eternity.'

Fey was so happy at Second City that she had doubts about moving to New York when Lorne Michaels invited her to join Saturday Night Live. The show, which started in 1975, has a reputation as a fearsome testing ground, especially for women, who had always been outnumbered by the men. The brutal and relentless weekly process by which sketches and jokes get winnowed down before the show can be devastating.

One thing Fey learnt from her fellow comics on the show was that, 'If you want to make an audience laugh, you dress a man up like an old lady and push her down the stairs. If you want to make comedy writers laugh, you push an actual old lady down the stairs.'

The first sketch Fey wrote, about Bill Clinton, died in read-throughs. 'This weight of embarrassment came over me, and I felt like I was sweating from my spine out,' she recalls. 'But I realised, "OK, that happened, and I didn't die". You've got to experience failure to understand you can survive it.'

Survive she did, and in 1999 Michaels made her head writer, the first woman to hold the post. The following year he made her co-host of the centrepiece 'Weekend Update' segment. Weekend Update features two faux newsreaders dissecting the previous week's news and disembowelling those unlucky enough to have been part of it.

'Prostitutes in Lyon, France, sent a fax to the government to complain that they are losing business to Eastern European women who are protected by the Albanian mafia,' said Fey in one typical segment. 'First of all, how rough-looking are these French prostitutes that all their customers are running to the Albanians? Secondly, why did they send a fax, and from whence? Do they have a fax machine in the whorehouse, or did they all trundle down to Kinko's - "You fax these, I'll let you shave me". Thirdly, how come French whores know how to work a fax machine, but every time I try to use it, I hit Powersave, or I forget to dial 9? This just proves what my boyfriend always says - that I'm dumber than a French whore.'

Other examples of Fey's Weekend Update repertoire: 'A Harvard Medical School study has determined that rectal thermometers are the best way to tell a baby's temperature. Plus, it teaches the baby who's boss.'

'Tom Cruise and Nicole Kidman say their split is amicable, and they want everyone to know that after their divorce their two adopted children will be returned to the prop department at Universal Studios.'

'In order to feel safer on his private jet, John Travolta has purchased a bomb-sniffing dog. Unfortunately, the dog came six movies too late.'

'U2 lead singer Bono met with President Bush on Wednesday and urged the president to help the world's poor, while the president urged Bono to get back with Cher.'

Under Fey's tutelage as head writer, the number of women on the show increased significantly. But Fey doesn't believe Saturday Night Live was ever overtly hostile to women, as long as they are funny. 'If it gets laughs it goes forward,' she says. 'There have been so many women who were stars on SNL. It's when they leave and try and be in the movies that things get hard.'

Which is why Fey is so thrilled that Baby Mama has been successful. 'Amy and I were excited to be doing a story about two women who are not somebody else's girlfriend,' says Fey. 'I liked the topicality of the fertility issues. There's so much weirdness and emotion about it. And Amy liked that it had nothing to do with a goddam wedding.'

Fey's hard-won success has also clearly squelched ludicrous charges, made recently by Hitchens and others, that women aren't funny. Responding to the late Michael O'Donoghue, the first head writer for Saturday Night Live, who once said that it helped to have 'a big hunk of meat between the legs' when writing humour, Fey says: 'I do have one, but it's been flayed open to a vagina.' So you don't agree? 'Well, the thing is, he said it and then he died. So, I don't know. '

But it's also clear that Fey's success is the exception in US comedy rather than the rule. Media historian Robert Thompson believes there are clear social reasons for that. 'Until relatively recently, the kind of things that would lead you to a life of comedy, just like the kind of things that would lead you to a life of crime, tended to be those things that were rewarded in boys, but not in girls. You could act up in school and you could be priming the act that you would eventually be doing professionally. It was kind of expected, boys will be boys. But for girls it was considered unfeminine, unseemly, even downright promiscuous.'

'She's pretty monastic at times,' says Poehler. 'She's not the first girl to belly-flop into the pool at the pool party. She watches everybody else's belly-flops and then writes about it.'

As Lorne Michaels, who has worked with comedians for more than three decades, looks at Fey's career in the light of the success of 30 Rock and Baby Mama, I ask him if it really is harder for women to establish an enduring comedy persona. 'They have less time,' he says. 'If they want it all, they've got to know who they are fast. There's no wandering around in a haze for 10 years.'

And you sensed that Tina knew who she was? 'From the very beginning,' he says. 'I think she wanted it all, and if she doesn't get it all she's going to get most of it.'